#16 - Local, Must Be True

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=17159)

The correct answer choice is (D)

The question stem stipulates that exactly two rubies are selected. Of course, the first rule states that at least two topazes are selected, resulting in the following initial scenario:

D00_Game_#3_#16_diagram 1.png

The last two stones appear to be undetermined, but because of the second rule, they cannot be two sapphires. That leaves only two apparent choices for the remaining two stones: two topazes, or one topaz and one sapphire. But, adding two topazes would mean all four topazes are selected, which is impossible due to the third rule. Thus, the remaining two stones must be one topaz and one sapphire, resulting in the following setup:

D00_Game_#3_#16_diagram 2.png

Hence, answer choice (D) is proven correct.

[srcline@noctrl.edu]

Hello

I am having difficulty with question 16. Here are my initial inferences:

W H
W Z
M H

So for question 16 is this the opposite of rule 2? Instead of two sapphires, its two rubies? How would I go about solving this problem, because its a must be true, so would you use a hypothetical?

Thank you
Sarah

[Lucas Moreau]

Hello, srcline,

Your first two inferences are robust, but I think your third one could be a little more specific. It's true that M H, but it is also true that M Z for the same reason. I would style it like this instead:

W H
W Z
M W Not!H and Not!Z

For number 16, it's best to use hypotheticals here. If you have two rubies selected, then you have four possibilities:

Exactly zero sapphires are selected,
Exactly one sapphire is selected,
Exactly two sapphires are selected, or
Exactly three sapphires are selected.

It cannot be true that exactly two sapphires are selected, because two sapphires and two rubies violates Rule 2. And it cannot be true that exactly zero sapphires are selected, as that would necessitate all four topazes to be selected, and that's impossible - if W is selected, Z is not, so you can't have all four topazes. It further cannot be true that exactly three sapphires are selected, because that would mean only one topaz can be selected (2 + 3 + 1), and one topaz violates Rule 1. Therefore, it must be true that exactly one sapphire is selected if two rubies are selected.

Hope that helps,
Lucas Moreau